Question

simplify the expression. assume that the den\\(\frac{f^{-2}g^{-4}}{h^{-5}}\\)

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) and \(\frac{1}{a^{-n}} = a^{n}\). We will apply this rule to each term in the numerator and the denominator.
For the numerator terms: \(f^{-2}=\frac{1}{f^{2}}\) and \(g^{-4}=\frac{1}{g^{4}}\). For the denominator term: \(\frac{1}{h^{-5}}=h^{5}\) (since \(\frac{1}{a^{-n}}=a^{n}\)).

Step2: Rewrite the expression

Substitute the negative exponents with their positive exponent equivalents. The original expression \(\frac{f^{-2}g^{-4}}{h^{-5}}\) can be rewritten as \(\frac{\frac{1}{f^{2}}\cdot\frac{1}{g^{4}}}{ \frac{1}{h^{5}}}\).

Step3: Divide by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{\frac{1}{f^{2}g^{4}}}{\frac{1}{h^{5}}}=\frac{1}{f^{2}g^{4}}\times h^{5}\).

Step4: Simplify the expression

Multiplying these together gives \(\frac{h^{5}}{f^{2}g^{4}}\).

Answer:

\(\frac{h^{5}}{f^{2}g^{4}}\)